I had installed opera with the deb package downloadable from Opera's site and it did not load HTML 5 videos from youtube. The only solution that worked for me was to uninstall the version I had with:
sudo apt-get remove --purge opera-stable
and then installed the version from the PPA package following this other AskUbuntu post.
Adding a pointer to the opera stable sources:
sudo sh -c 'echo "deb http://deb.opera.com/opera/ stable non-free" >> /etc/apt/sources.list.d/opera.list'
Install the key:
sudo sh -c 'wget -O - http://deb.opera.com/archive.key | apt-key add -'
Fetch the new repository:
sudo apt-get update
Install latest Opera with:
sudo apt-get install opera-stable
Now Opera is able to handle HTML5 videos.